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APPENDIX B SET OF GTOC3 ASTEROIDS Table 34 lists all of the asteroids in the full GTOC3 problem, including their SPK- ID number, common name, <strong>and</strong> orbital elements (semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of periapsis, mean anomaly, <strong>and</strong> epoch). The asteroids are sorted by their SPK-ID number. spkid name a (AU) Table 34: GTOC3 Asteroids. e i (deg) LAN (deg) arg. periapsis (deg) M (deg) epoch (MJD) 1 2004 ER21 0.900329 0.17105522 7.95592 357.43143 343.23658 52.625406 54200 2 1995 CR 0.906736 0.86845445 4.03569 342.77208 322.39782 328.3017003 54200 3 1992 BF 0.9080026 0.27176608 7.25394 315.47182 336.42045 54.111859 54200 4 2002 XY38 0.9096341 0.21765254 2.09641 159.63529 119.41817 141.6151818 54200 5 1999 AO10 0.911399 0.11078484 2.62269 313.33854 7.63927 309.5515364 54200 6 2000 WO107 0.9114029 0.78065556 7.7829 69.37362 213.58377 169.2181562 54200 7 2006 BA9 0.9125604 0.3659925 8.31532 305.97027 25.50724 269.3288907 54200 8 2001 HY7 0.9139376 0.41209549 5.20961 205.38304 211.00626 69.2586068 54200 9 2001 RV17 0.9140581 0.34250016 7.52263 154.12079 4.35647 343.2637171 54200 10 1989 UQ 0.9152487 0.26483239 1.29152 178.29646 15.0241 189.1719934 54200 11 2000 LG6 0.9163425 0.11221324 2.83037 72.72983 7.8651 102.1739718 54200 12 2003 CA4 0.9203666 0.1197246 7.47925 139.95566 172.94835 86.6971188 54200 13 2004 RX10 0.9204306 0.35114382 5.9586 173.89189 333.85636 186.4545742 54200 14 2002 EM7 0.9212257 0.36304986 1.54747 347.21646 57.6856 354.1537351 54200 15 Apophis 0.9222614 0.19105942 3.33131 204.45915 126.38557 307.3630785 54200 16 2005 TG50 0.9238455 0.13388842 2.42676 346.04551 199.60593 81.9756648 54200 17 2002 JR100 0.924675 0.29782641 3.76334 203.5673 253.42378 293.6715722 54200 18 1992 FE 0.9272536 0.40535098 4.79702 311.9926 82.42602 52.7808967 54200 19 2000 SZ162 0.9294449 0.16754816 0.89598 14.74941 131.30472 336.3249638 54200 20 2002 TZ66 0.9300326 0.12059229 8.47831 13.13956 223.06212 135.7560272 54200 21 2003 YS17 0.9303548 0.31304457 6.52409 99.17972 134.4818 133.8075539 54200 22 2006 VX2 0.9330736 0.29005873 9.86637 47.38582 126.40932 69.0741375 54200 23 2005 FN 0.9330778 0.33020963 3.74806 177.42092 120.83813 18.9011538 54200 24 2002 OA22 0.9359164 0.24295478 6.90562 174.41213 318.28487 205.6768657 54200 25 1999 AQ10 0.937275 0.23448424 6.55836 327.40416 299.49467 250.5925532 54200 26 2000 EW70 0.9376817 0.32110421 5.41918 178.31485 125.311 188.0399576 54200 27 2001 CQ36 0.9396849 0.17623802 1.29202 31.94641 342.49359 22.9155357 54200 28 2001 BA16 0.9403125 0.13737419 5.76859 115.61889 242.8389 42.1907675 54200 29 2004 QD14 0.9426399 0.33810282 6.25178 75.45204 109.28368 66.0525408 54200 30 2004 VJ1 0.9437535 0.16446907 1.29373 233.53809 332.36301 75.2928449 54200 31 2005 VN5 0.9447613 0.23312124 2.08656 49.35063 115.04505 102.617135 54200 32 2006 TS7 0.9466118 0.57983607 5.46456 225.45909 299.72601 103.8271836 54200 33 2001 SQ263 0.9480374 0.49151246 3.95115 327.30349 262.3598 78.649304 54200 34 2005 TE49 0.9492487 0.37694757 5.00558 195.25531 304.934 276.7190717 53652 35 2006 SF6 0.9493911 0.28039283 5.86507 228.16645 305.51522 43.6895559 54200 177
36 2006 RJ1 0.9508113 0.30070707 1.4145 93.51404 110.28027 349.5007972 54200 37 2004 QA22 0.9508977 0.12172568 0.57414 175.15217 28.54873 55.2451141 54200 38 2001 TD 0.9541288 0.16608077 9.01107 13.21665 241.33953 68.8170052 54200 39 2004 UH1 0.9541748 0.39680796 3.71292 29.85969 120.62228 155.2936477 54200 40 2006 FH36 0.9544687 0.1986 1.59072 280.91015 154.77967 128.0764061 54200 41 2002 LY1 0.9550094 0.37931534 2.9091 248.2326 133.96031 338.4972621 54200 42 2005 UV64 0.9580862 0.11600696 5.41663 216.09819 313.93026 71.146594 54200 43 2005 GE60 0.9588639 0.24584744 5.56845 229.9559 112.69363 285.2220831 54200 44 2004 RO111 0.9611941 0.32883148 5.33444 199.44692 280.82215 164.3568742 54200 45 1998 HD14 0.9630822 0.31264453 7.80717 183.96655 260.73453 261.9364311 54200 46 2004 UT1 0.9644067 0.22113792 4.50799 211.98171 294.22407 123.9756016 54200 47 2003 YG136 0.968992 0.35504091 2.7352 86.5446 127.9831 81.832236 54200 48 2005 QP11 0.9755418 0.1757465 3.95693 334.92822 119.64718 142.418984 54200 49 2000 SG344 0.9774002 0.06697124 0.11024 192.31139 274.9223 180.3781477 54200 50 2002 CQ11 0.9788526 0.42841032 2.45977 81.43849 272.76681 200.8820974 54200 51 2002 CD 0.9798418 0.17672247 6.87919 8.74939 331.55652 254.4324731 54200 52 1996 XZ12 0.9799732 0.49926135 5.65852 251.74134 55.81636 72.9065206 50427 53 1998 XN17 0.9818487 0.20968172 7.24543 85.99494 226.33101 308.1410001 54200 54 2006 AM4 0.9818736 0.649191 4.12836 123.29217 139.66996 15.6480498 54200 55 2001 FR85 0.9826891 0.02793117 5.24394 183.09543 233.53197 194.9601844 54200 56 2002 VX91 0.9846133 0.20141992 2.33173 216.8382 78.23357 274.8314614 54200 57 2000 OK8 0.9847498 0.22112979 9.98502 304.63783 166.12112 153.7352685 54200 58 2006 HR29 0.9852749 0.26346811 9.54116 232.80061 212.57562 87.7117748 54200 59 2006 SU217 0.9858344 0.17456034 2.64217 194.38475 38.23562 311.7733113 54200 60 2002 FT6 0.9882602 0.46273082 9.48968 188.6153 226.6889 122.5236582 54200 61 2006 QQ56 0.9883457 0.04505596 2.7989 161.62964 330.03731 70.0709228 54200 62 2004 EW 0.9894133 0.27979222 4.66406 343.43945 55.79267 142.6799405 54200 63 Khufu 0.9894148 0.46856366 9.91863 152.50644 54.98951 71.2602183 54200 64 2003 WP25 0.9907792 0.12120994 2.52245 42.1994 224.96577 297.5344418 54200 65 2005 CN61 0.9907967 0.06870481 9.52323 146.97133 248.33039 166.3675529 54200 66 2003 YN107 0.9927025 0.01393412 4.30184 264.84372 80.48505 217.7923676 54200 67 2005 UH6 1.0006444 0.63236792 2.64874 19.21603 200.24778 235.9241374 54200 68 2006 FV35 1.0010847 0.37754605 7.09998 179.61929 170.85813 226.9041918 54200 69 2000 EE104 1.0047041 0.29345413 5.24196 25.96806 280.93086 266.5400007 54200 70 2000 PH5 1.0051359 0.2301559 1.60139 278.41759 278.53077 327.3858309 54200 71 2001 GO2 1.0064333 0.16803052 4.61512 193.60694 265.29267 63.1828205 54200 72 2001 XX4 1.0065836 0.55673375 0.84697 127.00806 186.85712 159.7164678 54200 73 2005 TC51 1.0075124 0.3055468 5.66968 199.48658 288.09442 97.8673657 54200 74 1999 JV6 1.0075874 0.31111687 5.31393 124.62191 235.56835 198.4820189 54200 75 2000 QX69 1.0104975 0.27149424 4.58184 150.52076 73.62628 265.8465193 54200 76 2006 JY26 1.011128 0.08427146 1.42373 45.04477 277.02812 241.3233221 54200 77 2005 WK4 1.0116893 0.23719672 9.8329 138.33302 74.39146 357.2955237 54200 78 2002 PN 1.014505 0.0689143 9.14377 309.5259 107.45923 113.1536664 54200 79 2005 CN 1.0160246 0.18501785 2.31341 308.83895 321.30873 287.5129436 54200 80 2000 AG6 1.0176695 0.1899321 2.43499 283.11721 276.29949 318.9700596 54200 81 2002 TY59 1.0191848 0.23375184 6.6107 9.84962 259.11368 214.0602972 54200 82 2001 FC58 1.0201136 0.34316691 6.76713 174.76709 261.06877 26.774746 54200 83 Asclepius 1.0223202 0.35703111 4.9126 180.39166 255.1881 230.9053982 54200 84 1998 MW5 1.0228657 0.36267778 6.28735 80.47794 26.63877 320.6303075 54200 85 2006 BZ147 1.023656 0.09861161 1.40819 140.15053 95.17529 318.8393785 54200 86 2006 EK53 1.0251033 0.51704999 2.2214 5.21615 41.17404 67.9974415 53808 87 2005 BG28 1.0257488 0.22716044 6.13219 313.53121 80.85145 108.3498278 54200 88 1991 VG 1.0268385 0.04918621 1.44562 73.9738 24.50924 245.9824779 54200 89 2006 BJ55 1.0270842 0.1282408 5.94186 307.70442 288.23104 323.2412364 54200 90 2006 DQ14 1.0276275 0.05302857 6.29663 155.36066 292.38941 89.799583 54200 178
Page 1 and 2:
DESIGN SPACE PRUNING HEURISTICS AND
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“The mediocre teacher tells. The
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I am thankful for all of my friends
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2.5 Small Sample Problem...........
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LIST OF TABLES Table 1 Ten best ast
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LIST OF FIGURES Figure 1 Mars round
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Figure 35: Low-thrust optima as a f
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LIST OF SYMBOLS AND ABBREVIATIONS A
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σBXB υ φ ω Ω Sample standard d
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optimization scheme to locate a bro
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provide clues to the nature of the
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additional constraints and objectiv
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Pontryagin’s Minimum Principle, w
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improved accuracy (as compared to d
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Figure 2: Trajectory structure of t
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flyby problems with numerous interm
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Gravity assists are modeled as inst
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Prior to the LTTT effort, the prima
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the shape of the trajectory and ana
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draws upon the theory of niche and
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the sequence of encounter bodies, t
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1.2.2 Evolutionary Neurocontrollers
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Figure 6: Converting an evolutionar
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which find good solutions but can n
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functions. In this problem, only im
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As aforementioned, branch-and-bound
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consuming, user-intensive, and ofte
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asteroid tour mission design proble
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CHAPTER II DEVELOPMENT OF METHODOLO
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Kˆ ĥ i ν ê v r ω Ĵ Ω nˆ Î
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Finally, both the eccentricity of a
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maximum possible number of revoluti
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outer loop: a genetic algorithm and
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2.3.2 Branch-and-Bound The branch-a
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The order in which the branches are
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approach performs best, followed by
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Figure 16: Effect of number of segm
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Within the sample problem, MALTO wa
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Table 2: Orbital elements of astero
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final mass. The correlation coeffic
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Maximum Final Mass (kg) 1500 1250 L
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The next approach is to compare the
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Final Mass (kg) 950 900 850 800 750
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pruning metric must be calculated f
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educed-size problem. Furthermore, t
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aBiB < 25%, and 15% for Leg 1, Leg
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Earth departure date and three time
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algorithm, which determines the opt
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is calculated using the same specif
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metrics which were calculated in th
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sorted by final mass. All of the se
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impulse optima. Figure 35 plots the
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CHAPTER III OVERVIEW OF METHODOLOGY
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(1) All asteroid sequences are rank
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two-impulse optimum solutions. Ther
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identifying another metric that cou
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CHAPTER IV VALIDATION OF METHODOLOG
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Table 8 lists the 10 best asteroid
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In order to further validate the pr
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impulse ∆V). The first iteration
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Because the impulsive multiplier ha
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Table 12: Effectiveness of the meth
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function calls to MALTO were requir
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order of 0.8 (assuming a final mass
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Table 16: Design variables for gene
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known solution to 1621 kg. Based on
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MBfB (kg) #1, #63, and #16, respect
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problem (Table 17). Additionally, t
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≤ Inclination (deg) 60 50 40 30 2
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order to have a benchmark with whic
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Of the remaining sequences, the 1 s
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Table 22: Settings for the genetic
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Page 147 and 148: of exactly four weeks. As a benchma
Page 149 and 150: Objective Function (kg/yr) 120 100
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Page 153 and 154: asteroid sequences would be require
Page 155 and 156: Table 27: Best known solutions rema
Page 157 and 158: Table 29: Best known solutions rema
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Page 161 and 162: heuristics chosen were based on the
Page 163 and 164: problem, the best set of solutions
Page 165 and 166: Finally, for each set of inner loop
Page 167 and 168: solutions from the GTOC2 competitio
Page 169 and 170: sequences were optimized in low-thr
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Page 173 and 174: types of the TSP, they have not bee
Page 175 and 176: methodology would be applied in the
Page 177 and 178: APPENDIX A SET OF GTOC2 ASTEROIDS T
Page 179 and 180: 3054373 "2000 UK11" 0.88325596 0.24
Page 181 and 182: 3152317 "2003 GQ22" 0.87232869 0.18
Page 183 and 184: 3283227 "2005 MR5" 0.85281863 0.295
Page 185 and 186: 2000089 Julia 2.5500653 0.18377079
Page 187 and 188: 2000496 Gryphia 2.1987751 0.079568
Page 189 and 190: 2001216 Askania 2.2322234 0.1793551
Page 191 and 192: 2000134 Sophrosyne 2.5632069 0.1166
Page 193 and 194: 2000712 Boliviana 2.5738464 0.18812
Page 195: 2005209 "1989 CW1" 5.1533221 0.0495
Page 199 and 200: REFERENCES [1] Rayman, M.D., Willia
Page 201 and 202: [20] Hargraves, C. R., and Paris, S
Page 203 and 204: [38] Petropoulos, A., Kowalkowski,
Page 205 and 206: [57] Wuerl, A., Crain, T., Braden,
Page 207 and 208: [78] Cosmic Vision: Space Science f
Page 209: time, she enjoys traveling as well
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